The free product of residually finite groups amalgamated along retracts is residually finite

Boler, James; Evans, Benny

doi:10.1090/S0002-9939-1973-0306329-3

The free product of residually finite groups amalgamated along retracts is residually finite
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by James Boler and Benny Evans

Proc. Amer. Math. Soc. 37 (1973), 50-52

DOI: https://doi.org/10.1090/S0002-9939-1973-0306329-3

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Abstract:

It is shown that residual finiteness is preserved by the generalized free product provided that the amalgamated subgroups are retracts of their respective factors. This result is applied to knot groups. The outcome is that the question of residual finiteness for knot groups need only be answered for prime knots.

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